Ternary Magnesium Rhodium Boride Mg Rh B with a Modified Y -Type Crystal...

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Ternary Magnesium Rhodium Boride Mg 2Rh1-xB6+2x with a ModifiedY2ReB6-Type Crystal Structure

A. M. Alekseeva, †,‡ A. M. Abakumov, †,‡,§ P. S. Chizhov, †,‡ A. Leithe-Jasper, † W. Schnelle, † Yu. Prots, †

J. Hadermann, § E. V. Antipov, ‡ and Yu. Grin* ,†

Max-Planck-Institut fu¨r Chemische Physik fester Stoffe, No¨thnitzer Strasse 40, 01187 Dresden,Germany, Chemistry Department, Moscow State UniVersity, Moscow 11992, Russia, and EMAT,UniVersity of Antwerp, Antwerp B-2020, Belgium

Received March 7, 2007

The new ternary magnesium rhodium boride Mg2Rh1-xB6+2x has been prepared by the reaction of the mixture ofMg powder, RhB, and crystalline boron in a Ta container sealed under argon. The crystal structure of Mg2Rh0.75(1)B6.50(4)

is determined using single-crystal X-ray diffraction, electron diffraction, and high-resolution electron microscopy(space group Pbam, a ) 8.795(2) Å, b ) 11.060(2) Å, c ) 3.5279(5) Å, Z ) 4, 630 reflections, RF ) 0.045). Itrepresents a modified Y2ReB6 structure type with an unusual replacement of part of the Rh atoms by boron pairslocated in the pentagonal channels parallel to the c axis. The pairs interconnect the neighboring planar boron netsinto the 3D framework. The variation of the lattice parameters reveals a homogeneity range Mg2Rh1-xB6+2x. Therandom distribution of the Rh atoms and boron pairs and the stabilizing effect of the boron pairs on the Y2ReB6

type structure motif are discussed using electronic band structure calculations and chemical bonding analysis withthe electron localization function (ELF).

Introduction

The Y2ReB6 structure type is one of the prevalent structuretypes among the ternary transition metal borides with highboron content. The crystal structure of Y2ReB6 (space groupPbam, a ) 9.175 Å,b ) 11.55 Å,c ) 3.673 Å)1,2 can bedescribed as an alternation along thec-axis of distorted close-packed layers of the metal atoms and planar boron netsformed by pentagonal, hexagonal, and heptagonal rings. Thisstructure type is common for boron-rich ternary compoundsof 4d and 5d transition metals (M) in the RE-M-B systems,where RE) U, Pu, Y, Gd, Tb, Dy, Ho, Er, Tm, Yb, and Luand M) Mo, W, Tc, Re, Ru, and Os.1-12 There are only afew representatives of the Y2ReB6 type among the ternary

borides of rare-earth metals with 3d transition metals(Lu2FeB6,13 Sc2CrB6,14 Lu1.34V1.66B6,15 Er(V0.77Ta0.23)VB6

16)and aluminum (Sc2AlB6,17,18 Yb2AlB6,19,20 Lu2AlB6

21). In

* To whom correspondence should be addressed. E-mail:[email protected].

† Max-Planck-Institut fu¨r Chemische Physik fester Stoffe.‡ Moscow State University.§ University of Antwerp.

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Inorg. Chem. 2007, 46, 7378−7386

7378 Inorganic Chemistry, Vol. 46, No. 18, 2007 10.1021/ic7004453 CCC: $37.00 © 2007 American Chemical SocietyPublished on Web 08/09/2007

contrastto Re, Ru, and Os, compounds with Rh and Ir withthis structure type are only known with scandium: Sc2RhB6

and Sc2IrB6.22

The interest in structures based on planar boron nets hassignificantly increased due to the important role of such netsfor the superconducting behavior of MgB2.23 Several typesof topologies of planar boron nets are known up to now,among them hexagonal graphite-like nets in the AlB2

structure, the nets formed by pentagonal and heptagonal ringsin YCrB4

24 and ThMoB4,25 and the mixed boron netscorresponding to the Y2ReB6 structure type described above.

On the basis of the size criterion, the AMB4 (A ) alkaline-earth metal) borides with YCrB4/ThMoB4-type structureshould be stable ifrA/rM > 1.30, whereas the A2MB6 borides(Y2ReB6 structure type) require therA/rM ratio to be lowerthan 1.30.14 This points out the possibility of the formationof Y2ReB6-type borides in Mg-M-B systems with M)Rh, Ru, Re, and Os (rMg/rM > 1.16-1.19).

In this work we report the synthesis and characterizationof the new ternary boron compound of magnesium andrhodium with the Y2ReB6-like crystal structure.

Experimental Section

Starting Material and Synthesis Procedure. Magnesiumpowder (Alfa Aesar, 99.8%), rhodium powder (Chempur, 99.9%),and crystalline boron (Alfa Aesar, 99.999%) were used as the initialreagents. To improve the reactivity of the crystalline boron, thefraction with particle size smaller than 25µm was selected for thepreparation. All synthetic operations were performed in a gloveboxunder argon atmosphere (content of O2 and H2O e 0.1 ppm). Theoxygen content in the initial materials was analyzed by the gascarrier hot extraction method (combined infrared and heat-conduc-tion detector TC 436 DR/5, LECO). For the rhodium powder andthe crystalline boron the oxygen content was found to be lowerthan the detection limit (0.038 wt %). An oxygen content of 0.05-0.20 wt % was found for different batches of the magnesiumpowder.

Taking into account the low reactivity and high melting pointsof Rh metal (Tm(Rh) ) 1966°C)26 and crystalline boron (Tm(Bcr)) 2300°C)26, we used the rhodium monoboride (Tm ) 1250°C)27

as a precursor for synthesis. Single-phase material with thecomposition RhB was prepared by arc-melting of the stoichiometricmixture of rhodium and boron powder under argon atmosphere.The obtained monoboride was ground in a tungsten carbide mortarand mixed with appropriate amounts of Mg powder and crystallineboron in an agate mortar, pressed into pellets, and sealed intotantalum containers (diameter 8 mm, length 25 mm). The tantalumcontainers were sealed into evacuated silica ampules and annealedat 850-1250°C for 3-20 days with several intermediate regrind-ings in argon atmosphere. The ampules were finally quenched inwater.

Differential Thermal Analysis (DTA). DTA was carried outin the range from room temperature to 1300°C (STA 409, Netzsch,30-60 mg/sample) in niobium containers sealed in argon atmo-sphere with a heating rate of 10 K/min.

X-ray Powder Diffraction. Phase identification and latticeparameter determination were performed from room-temperatureX-ray powder diffraction data (Huber G670 Image Plate Guiniercamera, CuKR1 radiation,λ ) 1.540598 Å) with LaB6 as an internalstandard (a ) 4.15692 Å) for refinement of the unit cell parameters.The program packages WinCSD28 and WinXPow29 were used forprocessing of the powder data.

X-ray Single-Crystal Diffraction. Single crystals suitable forX-ray data collection were selected from a sample with nominalcomposition Mg2RhB annealed at 1000°C for 5 days withsubsequent furnace cooling. The diffraction experiment wasperformed on a Rigaku AFC-7 four-circle system with MercuryCCD detector. Absorption correction was made using a multiscanprocedure. Crystallographic information and details on the datacollection are given in Table 1. The program package WinCSD28

was used for the structure solution and refinement.Metallography and Energy Dispersive X-ray Analysis (EDX).

The metallographic investigation was performed on polishedsamples with a Zeiss Axiotec 100 optical microscope equipped withpolarizer and analyzer and located in an argon-filled glovebox.30

The chemical compositions of the bulk sample and of the singlecrystal used for the diffraction experiment were analyzed with aPhilips XL30 scanning electron microscope equipped with anEDAX Phoenix detector. EDXS measurements were performed witha standardless method on MgK and RhL lines at 5-7 points foreach phase.

Measurements of Physical Properties.The magnetic suscep-tibility was measured in a SQUID magnetometer (Quantum DesignMPMS-XL7) in various external fields down to 1.8 K on a smallpolycrystalline sample. A correction for a ferromagnetic traceimpurity (corresponding to<10 µg of Fe metal/g) was done usingthe Honda-Owen extrapolation. The electrical resistivity wasdetermined in a standard dc four-point setup on a bar-shapedsintered powder sample in a temperature range between 3.8 and320 K.

(21) Okada, S.; Yu, Y.; Lundstro¨m, T.; Kudou, K.; Tanaka, T.Jpn. J. Appl.Phys.1996, 35, 4718.

(22) Salamakha, P. S.; Rizzoli, C.; Salamakha, L. P.; Sologub, O. L.;Goncalves, A.; Almeida. M.J. Alloys Compd.2005, 396, 240.

(23) Nagamatsu, J.; Nakagava, N.; Muranaka, T.; Zenitani, Y.; Akimitsu,J. Nature2001, 410, 63.

(24) Kuz’ma, Yu. B.Kristallografiya 1970, 15, 372 (in Russian).(25) Rogl, P.; Nowotny, H.Monatsh. Chem.1974, 105, 1082.(26) Emsley, J.The elements; Oxford Chemistry Guides: London, 1991.(27) Oborowski, W.Metall (Isernhagen, Ger.)1963, 17, 108.

(28) Akselrud, L. G.; Zavalii, P. Yu.; Grin, Yu.; Pecharsky, V. K.;Baumgartner, B.; Wo¨lfel, E. Mater. Sci. Forum1993, 133-135, 335.

(29) STOE WinXPow, version 2.08; STOE & Cie GmbH: Darmstadt,Germany, 2003.

(30) Burkhardt, U.Scientific report 2001/2002; Max-Planck.Institut fu¨rChemische Physik fester Stoffe: Dresden, Germany, Jan 2003; p 39.

Table 1. Data Collection and Crystallographic Information forMg2Rh0.75B6.5

composition Mg2Rh0.75B6.5

space group Pbama, Å 8.795(2)b, Å 11.060(2)c, Å 3.5279(5)V, Å3 343.2(2)Z 4radiation; wavelength, Å Mo KR; 0.71073max. sinθ/λ 0.75calculated density, g cm-3 3.79absorption coefficient, cm-1 38.16measured reflections 2537independent reflections 630Req 0.072reflections used for refinement 531no. of parameters refined 42extinction coefficient 0.00021RF, wRF2 for F(hkl) g 6σ(F) 0.045, 0.058

Ternary Magnesium Rhodium Boride Mg2Rh1-xB6+2x

Inorganic Chemistry, Vol. 46, No. 18, 2007 7379

Calculation Procedure. The electronic structure of theMg2Rh1-xB6+2x compound was calculated for two ordered models:Mg2RhB6 and Mg2Rh0.5B7. For the first case the symmetrycoincides with the symmetry of the original structure (Pbam); forthe second case an ordered model with lower symmetry (P21am)was employed. The TB-LMTO-ASA31 program package was usedfor the calculations; a Barth-Hedin32 exchange-correlation potentialwas applied. The calculations were made for 16k-points in theirreducible wedge of the Brillouin zone. The integration over theBrillouin zone was performed using the tetrahedron method with72 inequivalent tetrahedra.

Both mentioned models are nearly close-packed, so it waspossible to avoid empty spheres addition in all cases.33 The radiiof the Rh spheres were 1.563 and 1.556 Å; the Mg sphere radiivaried in the range 1.600-1.910 Å for different positions in differentstructures, and the B sphere radii were varied in the range 0.958-1.038 Å. A basis set containing Mg(3s,3p), Rh(5s,5p,4d), andB(2s,2p) orbitals was employed for the self-consistent calculationswith Mg(3d), Rh(4f), and B(3d) functions being downfolded.

The electron localization function (ELF,η) was evaluatedaccording to Ref. 34 with the intrinsic procedure of the TB-LMTO-ASA package. To get more insight into the bonding situation inMg2Rh1-xB6+2x, the topology of the ELF was analyzed using theprogram BASIN,35 with subsequent integration of the electrondensity (ED) inside the corresponding ELF basins, like it wasproposed for the electron density within the AIM approach.36 Thisprocedure allows determining the electron counts for the atomiccore shells and the bonding attractors.

Transmission Electron Microscopy.Electron diffraction pat-terns were recorded on a Phillips CM20 microscope, and high-resolution images, on a JEOL 4000 EX. Simulations were madeusing the software package MacTempas.

Results and Discussion

The best nearly single-phase sample of the new phase,most suitable for the physical measurements, was obtainedby heat treatment of a mixture of RhB, Mg, and B with theinitial composition Mg2Rh0.5B7 at 1000°C for 8 days andthen at 1200°C for 8 days followed by quenching in water.The X-ray powder diffraction data (Figure 1) show thepresence of the new orthorhombic phase with a small amountof MgO (∼3%, originating from the initial Mg powder) anda few additional nonindexed peaks with maximum intensityof ∼3% of the strongest observed reflection. The X-raypowder diffraction pattern was indexed on a primitiveorthorhombic lattice with unit cell parametersa ) 8.752(1)Å, b ) 11.056(2) Å, andc ) 3.5874(7) Å. The latticeparameters, observed extinction conditions, and intensitydistribution indicated that the new phase belongs to theY2ReB6 structure type. From metallographic analysis andEDXS investigation, the majority phase with the Mg/Rh ratio

of 3.4(3) was found together with a small amount of MgOand an additional phase of which the composition could notbe precisely determined due to the very small particle size.Thus, the EDXS analysis shows a higher magnesium/rhodium ratio in the new phase compared to the A/M) 2ratio in the Y2ReB6-type structure. No other elements weredetected in the products.

The crystal structure of Mg2Rh0.75B6.5 was determinedusing X-ray single-crystal diffraction data (cf. ExperimentalSection). The atomic coordinates from the crystal structureof Y2ReB6 were chosen as starting values for the refinement.However, the refinement resulted in relatively large valuesof the reliability factors (RF ) 0.090,wRF2 ) 0.144) and inan unusually high value of the atomic displacement parameter(ADP) for the Rh position. This suggested the presence ofvacancies in the Rh position. The EDXS analysis of thesingle crystal revealed the Mg/Rh ratio of 2.74(5), inagreement with the Rh deficiency. Refinement of theoccupancy factor for the Rh position led to the value of 0.75-(1). With this occupancy the ADP for the Rh positiondecreased to a reliable value. The reliability factors alsodecreased toRF ) 0.059 andwRF2 ) 0.076. However,additional maxima of the difference Fourier map (3.2 e-/Å3)were found above and below the Rh atom along [001] (Figure2a). The refinement of the ADP for the Rh atom inanisotropic approximation did not reduce these residual peaksin the difference Fourier map. The distances between thepositions of the additional maxima and between thesepositions and neighboring boron atoms belonging to theexisting planar nets atz ) 0.5 were between 1.72 and 1.77Å. Such interatomic distances are typical for boron-boroncontacts. Therefore, it was assumed that the residual peaksof electron density correspond to a pair of boron atoms (B7).The center of mass for the B-B pair occupies the sameposition as the Rh atom. Finally, the occupancy anddisplacement parameters for the Rh atom were refinedsimultaneously with occupancy for the boron position B7.Biso(B7) was fixed at 0.5 Å2 because of the instability of therefinement caused by large difference in scattering powerbetween 1.25 for 0.25 B and 33.75 electrons for 0.75 Rh

(31) Jepsen, O.; Burkhardt, A.; Andersen, O. K.The TB-LMTO-ASAProgram, version 4.7; Max-Planck-Institut fu¨r Festkorperforschung:Stuttgart, Germany, 1999.

(32) Barth, U.; Hedin, L.J. Phys. C1972, 5, 1629.(33) Andersen, O. K.;Phys. ReV. B 1975, 12, 3060.(34) Savin, A.; Flad, H. J.; Preuss, H.; von Schnering, H. G.Angew. Chem.

1992, 104, 185;Angew. Chem., Int. Ed.1992, 31, 185.(35) Kohout, M.Basin, version 2.3; Max-Planck-Institut fu¨r Chemische

Physik fester Stoffe: Dresden, Germany, 2001.(36) Bader, R. F. W.Atoms in molecules: a quantum theory; Oxford Univ.

Press: Oxford, U.K., 1999.

Figure 1. X-ray powder diffraction pattern of Mg2Rh0.5B7 (thermaltreatment: 8 days at 1000°C + 8 days at 1200°C). Reflections of theadmixture phases are marked with stars.

Alekseeva et al.

7380 Inorganic Chemistry, Vol. 46, No. 18, 2007

located close to each other. Such refinement converged atoccupancy factors for the Rh and B7 positions of 0.75(1)and 0.25(2), respectively, and at significantly lower valuesfor the reliability factors (RF ) 0.045,wRF2 ) 0.058). Thevalue of the largest residual peak of electron densitydecreased to 0.98 e-/Å3 (Figure 2b). The final atomicparameters are listed in Table 2, and the interatomic distancesare given in Table 3.

As a result of the structure refinement, the compositionof the compound has to be described as Mg2Rh1-xB6+2x,where x corresponds to the occupancy factor of the B7position. The Mg/Rh ratio obtained from the structurerefinement is 2.67(3), within one esd equal to the EDXSdata (Mg/Rh) 2.74(5)) on the investigated single crystal.The final composition is then described as Mg2Rh0.75(1)B6.50(4).The bulk powder material is, according to EDXS, even moreRh-depleted: Mg2Rh0.60(5)B6.80(5).

Simultaneous occupation of both the (x, y, 0.249) and (x,

y, 0.751) B7 sites (parts of the 8i position related by a mirrorplane) by boron atoms with a probability of 25% and Rhsite with a probability of 75% is equivalent to a presence ofeither the B-B pair or the rhodium atom. If either only the(x, y, 1/4) or only the (x, y, 3/4) position is occupied, theobtained occupancies results in a simultaneous presence ofthe Rh atoms and the B atoms either above or below the Rhwith nonphysically short RhB distances. The ordered dis-tribution of the Rh atoms and boron pairs may result in apossible superstructure. The reciprocal lattice was investi-gated using electron diffraction on the sample Mg2Rh0.6B6.8.The electron diffraction patterns taken along the mostrelevant zone axes are shown in Figure 3. All patterns canbe completely indexed with a primitive orthorhombic latticeand the unit cell parameters determined from X-ray powderdiffraction. The following reflection conditions were ob-served: 0kl, k ) 2n; h0l, h ) 2n. These conditions arecompatible with space groupPbam. The forbidden reflections0k0 with k * 2n andh00 with h * 2n present on the [001]pattern; both are caused by multiple diffraction, as wasconfirmed by the absence of these reflections on the [100]and [010] patterns. No signs of superstructure formationthrough ordered distribution of rhodium atoms and boronpairs were observed, confirming the results of the single-crystal structure determination.

The crystal structure of Mg2Rh1-xB6+2x (Figure 4a) repro-duces in general the features of the Y2ReB6 structure type.It can be described as a stacking the boron nets along [001]which are sandwiched by the metal atoms solely locatedabove and below the boron ring centers. One-quarter of theRh atoms are replaced by the B-B pairs. The plane boronnets are formed of pentagonal, hexagonal, and heptagonalrings (Figure 4b). The neighboring plane nets can beinterconnected by the (B7)2 pair instead of Rh, which leadsto the formation of pentagonal-pyramidal units (Figure 4c).These units are parts of the icosahedral B12 clusters in thecrystal structure of elementalR-boron (Figure 4d) or otherboron-rich phases like MgB4 (Figure 4e).37-39

The partial hierarchical replacement is relatively rareamong the crystal structures of intermetallic compounds. Theatom-by-pair replacement was found, e.g., in the TbCu7

compound.40 The atom-by-triangle substitution was observedrecently in several gallides: Eu1-xGa2+3x;41 Eu3-xGa8+3x;42

Sr3-xGa8+3x;43 YbGa2.63.44

The boron-boron distances within the planar nets varyin the range from 1.68 to 1.83 Å. This is comparable with

(37) Matkovich, V. I. Boron and Refractory Borides; Springer-Verlag:Berlin, Heidelberg, Germany, 1977.

(38) Hoard, J. L.; Hughes, R. E.The Chemistry of Boron and ItsCompounds; Muetterties, E. L., Ed.; J. Wiley: New York, London,Sydney, 1967; p 25.

(39) Guette, A.; Naslain, R.; Galy, J.C. R. Acad. Sc. Paris1972, 275, 41.(40) Buschow, K. H. J.; Groot, A. S. Acta Crystallogr.1971, B27, 1085.(41) Sichevich, O.; Ramlau, R.; Giedigkeit, R.; Schmidt, M.; Niewa, R.;

Grin, Yu.Abstracts of the 13th International Conference on Solid StateCompounds of Transition Elements, Stresa, Italy, 2000; p O-13.

(42) Sichevich, O.; Prots, Yu.; Grin, Yu.Z. Kristallogr.sNew Cryst. Struct.2006, 221, 265.

(43) Haarmann, F.; Prots, Yu.; Go¨bel, S.; von Schnering, H.Z. Kristallogr.sNew Cryst. Struct.2006, 221, 257.

(44) Cirafici, S.; Fornasini, M. L.J. Less-Common Met.1990, 163, 331.

Figure 2. Difference electron density map in the vicinity of the Rh atomposition (isolines are drawn with a step of 0.3 e-/Å3, zero line is dashed):(a) without boron atoms in the B7 position; (b) with B7 atoms.



the double covalent radius of boron (rcov(B) ) 0.88 Å)26.The distances within the boron pair (B7-B7) and betweenthe B7 atoms and boron atoms from the boron nets are alsocomparable with 2rcov(B). The distances between the Mg andRh atoms are in accord with the sum of the metallic radii(r(Mg) ) 1.600 Å, r(Rh) ) 1.345 Å)26. The Mg-B andRh-B distances are approximately equal or slightly largerthan the sum of the radii.

Random distribution of the B-B pairs and the Rh atomsin their positions within the (001) plane was proven byHREM observation along [001]. On the [001] HREM imageof Mg2Rh0.6B6.8 (Figure 5a) the dark spots correspond to theprojection of the pentagonal rings of the boron nets; cf. thetheoretical image calculated at defocus∆f ) -50 Å and

thicknesst ) 40 Å (inset in Figure 5a) using the atomiccoordinates from Table 2. The dark spots corresponding tothe pentagonal channels are occasionally absent (as indicatedby the arrows in Figure 5b). This corresponds to the positionspreferentially occupied by the B-B pairs rather than the Rhatoms. The missing spots are randomly distributed, confirm-ing the lack of ordering in the (001) plane. The remarkabledifference in contrast occurs due to the drastic difference inscattering power between B and Rh (Figure 5c).

One may expect that the substitution of rhodium by boronpairs results in the formation of a Mg2Rh1-xB6+2x solidsolution. The homogeneity range of this solid solution wasinvestigated. The samples prepared from the mixture of RhB,Mg, and crystalline boron with initial compositionsMg2Rh1-xB6+2x (0 e x e 0.9) were consistently annealed at1000, 1200, and 1100°C for 7-10 days with intermediateregrindings. Despite the long annealing time, most of theprepared samples contained minor admixtures of one or twoternary phases (e.g., Mg1-xRhB,45 Mg3Rh5B2

46) and binaryphases MgO, Mg44Rh7,47 MgB4,39 and MgB2.23 Nevertheless,the lattice parameters of the Mg2Rh1-xB6+2x phase vary with

(45) Alekseeva, A. M.; Abakumov, A. M.; Leithe-Jasper, A.; Schnelle, W.;Prots, Yu.; Hadermann, J.; Van Tendeloo, G.; Antipov, E. V.; Grin,Yu. Z. Anorg. Allg. Chem.2005, 631, 1047.

(46) Nagelschmitz, E. A.; Jung, W.; Feiten, R.; Mu¨ller, P.; Lueken, H.Z.Anorg. Allg. Chem. 2001, 627, 523.

(47) Westin, L.Chem. Scr. 1971, 1, 127.

Table 2. Atomic Coordinates and Displacement Parameters (in Å2) forMg2Rh0.75B6.5

atom occ site x/a y/b z/c Beq/isoa

Mg1 4g 0.6794(4) 0.0846(3) 0 1.32(8)Mg2 4g 0.0547(4) 0.1265(3) 0 0.76(7)Rh 0.75(1) 4g 0.3594(1) 0.1809(1) 0 0.63(2)B1 4h 0.870(1) 0.1825(9) 1/2 0.6(1)B2 4h 0.248(1) 0.0783(9) 1/2 0.8(1)B3 4h 0.906(1) 0.0256(8) 1/2 0.5(1)B4 4h 0.446(1) 0.0640(8) 1/2 0.3(1)B5 4h 0.203(1) 0.2395(9) 1/2 0.4(1)B6 4h 0.522(1) 0.2121(8) 1/2 0.4(1)B7 0.25(2) 8i 0.359(2) 0.179(2) 0.249(7) 0.5b

atom B11c B22 B33 B12 B12 B13

Mg1 0.47(3) 0.48(3) 0.94(3) 0.01(3) 0 0Mg2 1.8(2) 0.9(1) 1.2(1) 0.1(1) 0 0Rh 0.6(1) 0.7(1) 1.1(1) 0.14(9) 0 0

a Beq ) 1/3[a*2a2B11 + b*2b2B22 + c*2c2B33 + 2aba*b*(cos γ)B12 +2aca*c*(cos â)B13 + 2bcb*c*(cos R)B23]; the displacement parameters forboron atoms were refined isotropically.b The isotropic displacementparameter for B7 atom was fixed (cf. text).c Anisotropic displacementparameter is defined as exp[-1/4(a*2h2B11 + b*2k2B22 + c*2l2B33 +2a*b*hkB12 + 2a*c*hlB13 + 2b*c*klB23)].

Table 3. Selected Interatomic Distances (Å) for Mg2Rh0.75B6.5

atoms distance atoms distance

Mg1-B2 2.601(8) Rh-B6 2.297(6)Mg1-B5 2.634(8) Rh-B2 2.315(6)Mg1-B6 2.649(7) Rh-B4 2.316(6)Mg1-B4 2.651(7) Rh-B1 2.324(7)Mg1-B1 2.663(7) Rh-B5 2.329(6)Mg1-B4 2.716(7)Mg1-B3 2.740(7) B1-B5 1.70(1)Mg1-Rh 2.956(4) B1-B3 1.76(1)Mg1-Rh 3.009(4) B1-B7 1.77(2)Mg1-Rh 3.039(4) B1-B6 1.77(1)Mg1-Mg2 3.305(5)Mg1-Mg2 3.333(5) B2-B7 1.72(2)Mg1-Mg2 3.378(5) B2-B4 1.75(1)Mg1-Mg1 3.5279(5) B2-B3 1.78(1)Mg1-Mg1 3.669(5) B2-B5 1.83(1)Mg2-B3 2.462(7) B3-B3 1.75(1)Mg2-B3 2.463(7)Mg2-B1 2.477(7) B4-B4 1.71(1)Mg2-B2 2.507(7) B4-B7 1.73(2)Mg2-B5 2.525(7) B4-B6 1.77(1)Mg2-B6 2.526(7)Mg2-Rh 2.736(4) B5-B6 1.68(1)Mg2-Rh 2.747(4) B5-B7 1.76(2)Mg2-B7 2.88(2)Mg2-B7 2.89(2) B6-B7 1.72(2)Mg2-Mg2 2.959(5) B7-B7 1.76(4)Mg2-Mg2 3.5279(5)

Figure 3. Electron diffraction patterns of Mg2Rh0.6B6.8.

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the initial composition: froma ) 8.7771(7) Å, b )11.063(1) Å, andc ) 3.5559(3) Å for x ) 0 to a )8.728(1) Å,b ) 11.034(3) Å, andc ) 3.618(1) Å forx )0.9. The variation of the lattice parameters confirms theexistence of the homogeneity range for the Mg2Rh1-xB6+2x

solid solution due to the replacement of the Rh atoms bythe boron pairs, corresponding to the reduction of the cellsize in the (001) plane and the expansion of the unit cell

along thec axis. Despite several attempts, the fully equili-brated samples of the solid solution were not obtained.Therefore, the exact region ofx in Mg2Rh1-xB6+2x was notestablished. The samples withx ) 0 and x ) 0.9 aredefinitely not single phases. Forx ) 1 the binary MgB4 phaseis known with its own crystal structure (Figure 4e).39 Thus,the homogeneity range is located betweenx ) 0 andx )0.9, in any case betweenx ) 0.25 andx ) 0.4.

Figure 4. Crystal structure of Mg2Rh0.75B6.5: (a) alternation of the atomic layers perpendicular to [001]; (b) [001] projection of the structure with fulloccupancy of the Rh position; (c) interconnection of the planar nets by the additional boron atoms in the B7 position; (d) pentagonal-pyramidal unitsin thecrystal structure ofR-boron; (e) pentagonal-pyramidal units in the crystal structure of MgB4.



Two models of the bonding pattern in Mg2Rh1-xB6+2x wereinvestigated: Mg2RhB6 with the unmodified Y2ReB6 struc-ture; Mg2Rh0.5B7 with ordered substitution of half of therhodium atoms by boron pairs (space groupP21am). In bothcases, the lattice parameters of Mg2Rh0.75B6.5 (Table 1) wereused.

The total electronic density of states (DOS) for bothmodels is presented on Figure 6. In both cases the Fermilevel lies in a pseudogap with very small value of DOS. Invicinity of EF, DOS is mainly constructed of B(p) states andRh(d) states. Since the DOS does not change remarkablywith rhodium-by-boron pair substitution, a further investiga-tion of the chemical bonding was undertaken using thecombined topological analysis of the electron localizationfunction and electron density.

The electron localization function for the Mg2RhB6 model(space groupPbam) is shown in Figure 7a. Each of the B-Bcontacts within the planar boron nets has an attractor in theELF representation revealing two-center bonding. All boronatoms are three-bonded. The presence of pentagonal, hex-agonal, and heptagonal boron rings and hence the differentbond lengths and angles inside the boron net are reflectedby the variation in their electron counts in the range of 2.43-3.23 e-. The electron counts do not correlate with theaccording interatomic distances, which is often for ELFrepresentations. Nevertheless, the average value of theelectron count for the whole net is 2.67 e-/bond, whichexactly matches the Zintl count, in contrast to 2.5 e-/B-Bbond found in the MgB2 compound48 but in agreement withthe results on AlB2.49 The formal charge of the crystallo-graphically different boron atoms (within the homolyticcleavage approach) varies from-0.94 to -1.15 with theaverage value of-1.02.

No unique attractors were found between Mg or Rh andthe boron atoms, indicating the ionic interaction between theanionic boron network and the cations. It should be notedthat, in contrast to this case, in other ternary magnesiumrhodium borides such as Mg1-xRhB45 and Mg8Rh4B50

covalent Rh-B interactions were observed. The charges ofthe Mg and Rh atoms for the Mg2RhB6 model were foundto be +2 within the accuracy of the calculations (Mg+1.96

and Rh+1.97).Thus, the formal electron balance for the Mg2RhB6 model

can be written as [Mg2+]2[Rh2+][B1-]6. A transfer of sixelectrons/formula unit from the metal atoms to the boron

(48) Schmidt, J.; Schnelle, W.; Grin, Yu.; Kniep, R.Solid State Sci.2003,5, 535.

(49) Burkhardt, U.; Gurin, V.; Haarmann, F.; Borrmann, H.; Schnelle, W.;Yaresko, A.; Grin, Yu.J. Solid State Chem.2004, 177, 389.

(50) Alekseeva, A. M.; Abakumov, A. M.; Leithe-Jasper, A.; Schnelle, W.;Prots, Yu.; Chizhov, P. S.; Van Tendeloo, G.; Antipov, E. V.; Grin,Yu. J. Solid State Chem.2006, 179, 2751.

Figure 5. [001] HREM image of Mg2Rh0.6B6.8 along [001]: (a)comparison of the experiment with the calculated image (inset), with unitcell indicated by a white rectangle and a scheme of the boron net; (b)pointlike defects (marked by arrows and with black rectangle) related tothe preferential occupation of the positions by boron pairs; (c) strong contrastchange along the region indicated with the white rectangle in (b).

Figure 6. Electronic density of states for the model structures Mg2RhB6

and Mg2Rh0.5B7. Partial contributions of the B7 atoms are highlighted onthe right side

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net is necessary. The formation of vacancies in the rhodiumposition leads to an electron deficiency in the polyanion thatshould be compensated, e.g., by implementing of B-B pairs.

To elucidate the changes in the chemical bonding withrhodium-by-boron pair substitution, the ELF distribution inthe Mg2Rh0.5B7 model (space groupP21am) was calculatedand analyzed (Figure 7b; the boron atoms connected to thepair (B7)2 are marked as Bi′). It demonstrates similar mainfeatures as in the Mg2RhB6 model. Covalent boron-boroninteraction exists in the boron network; magnesium andrhodium atoms do not form covalent bonds with boron. Theboron polyanion in the Mg2Rh0.5B7 model is formed by thethree-bonded boron atoms (B(3b)) from the planar nets, thefive-bonded boron atoms (B(5b)) forming the vertices of thepentagonal rings, and the six-bonded boron atoms (B(6b))constituting the boron pairs. The electron count for the bondsbetween the three-bonded boron atoms lies in the range of2.43-3.10 e-, with the average value of 2.69 e-, quite closeto that in the Mg2RhB6 model. The introduction of boron

pairs leads to additional bonds with much smaller electroncounts (Figure 7d,e). The electron counts for the B(5b)-B(5b) bonds are in the range 0.94-1.64 e- with the averagevalue of 1.29 e-/bond. The B(6b)-B(5b) boron-boroninteractions are characterized by smaller electron counts(0.60-0.78 e-/bond with the average value of 0.73 e-),whereas the B(6b)-B(6b) bond inside the pair is a simpletwo-electron bond. The average formal charges of boronatoms of different types calculated within the homolyticcleavage approach are-1.10 for three-bonded boron atoms,-0.44 for five-bonded boron atoms, and+0.08 for six-bonded boron atoms. Charges of Mg and Rh atoms remainthe same, as in the Mg2RhB6 model (Mg1.98+ and Rh1.97+).The distortion of the Rh outer core shell also does not changewith rhodium-by-boron pair substitution, confirming the samecharacter of the Rh-B interactions in both structures.

These data allow the deducing of the formal electronbalance for Mg2Rh0.5B7:

Figure 7. Electron localization function for the (a) Mg2RhB6 and (b) Mg2Rh0.5B7 models (isosurfaces withη ) 0.75 in yellow andη ) 0.65 in brown-orange shown). (c) ELF distribution and electron counts within the planar boron net in Mg2RhB6. (d) ELF distribution and electron counts within the planarboron network in Mg2Rh0.5B7. (e) B-B bonds in the pentagonal pyramidal unit and between boron atoms of the B7-B7 pair.



The appearance of the boron pairs instead of the Rh atomsand, hence, the formation of the 3D boron framework resultin a formal charge rearrangement within the boron frame-work, while the total electron transfer from the cations tothe boron polyanion does not change. Consequently, theboron pairs in the Mg2Rh0.5B7 structure stabilize the Y2ReB6

structure motif in case of Rh deficiency. In other words, theintroduction of the boron pair compensates the electrondeficiency caused by the appearance of the rhodium vacan-cies through the formation of covalent B-B bonds with lowelectron count. From this point of view, a homogeneity rangeMg2Rh1-xB6+2x may exist, which is supported by experi-mental results.

Replacement of the metal atoms by boron pairs may befavored by the smallrRE/rM ratio (RE) Sc, Y). Concerningthe lower boundary of this size ratio, the smallest knownvalue was found in the Sc2AlB6 compound (rSc/rAl ∼ 1.147).The structure of Sc2AlB6 was refined from single-crystalX-ray diffraction data with a slightly substoichiometricoccupation (90(1)%) of the Al position along with anisotropicdisplacement.17,18Small residual electron density peaks werealso observed above and below the Al position. These factsmay suggest that near or below the lower boundary of themetal size ratio the Y2ReB6 structure can be stabilized withboron-pair substitution.

The measurements of physical properties were performedon the good quality bulk sample mentioned above with theinitial Mg2Rh0.5B7 composition. Corresponding to the resultsof single-crystal structure solution and the results of theEDXS measurements performed for this sample, the com-position can be written as Mg2Rh0.6B6.8. The correctedmagnetic susceptibilityM(T)/H is diamagnetic and showstraces of paramagnetic impurities at low temperatures. At300 K a value of-85(50)× 10-6 emu‚mol-1 is found. Thus,no Pauli paramagnetic contribution is detected in

Mg2Rh0.6B6.8. No superconductivity or other phase transitionswere observed in the temperature range investigated.

The electrical resistivityF(T) of the compound (ca. 3.0mΩ cm at room temperature) varies only little with tem-perature (F(300 K) - F0 ≈ 0.2 mΩ cm). Interestingly, abroad rounded minimum ofF(T) is visible at ca. 45 K whichis followed by a gradual transition toward a linear increaseabove 120 K. The magnitude and the temperature dependenceof F(T) are reminiscent of a continuous metal-insulatortransition, which is additionally smeared out by the rhodium/boron pairs disorder. In tendency, this is in agreement withthe results of the band structure calculations, revealing anarrow pseudo gap for Mg2RhB6 composition and showingan increase of the DOS at Fermi level for Mg2Rh0.5B7.

Conclusions

The crystal structure of Mg2Rh1-xB6+2x represents a firstexample of a modified Y2ReB6 type structure. The randomreplacement of the rhodium atoms by boron pairs allows theadaptation of the crystal structure to the electron deficiencycaused by the vacancies in the rhodium position and to keepthe main structural motif. According to the chemical bondinganalysis with electron localization function, the electrondeficiency is compensated by the formation of the new B-Bcovalent bonds between the planar nets with lower electroncounts. In agreement with the band structure calculations,the compound is diamagnetic with a relatively high electricalresistivity.

Acknowledgment. We thank Dr. Gudrun Auffermannand Mrs. Ulrike Schmidt for the chemical analysis, Mrs.Susann Mu¨ller for the DTA/DSC, and Mr. R. Koban forphysical measurements. Dr. Ulrich Burkhardt is acknowl-edged for the metallographic analysis. Mrs. Katja Schulzeis thanked for the EDXS measurements. This work waspartially supported by the RFBR (Grant 06-03-33066-a).

Supporting Information Available: Structural, electrical re-sistivity, and magnetic susceptibility data. This material is availablefree of charge via the Internet at http://pubs.acs.org.

IC7004453

[Mg2+]2[Rh2+]0.5[B(3b)1.10-]3.5[B(5b)0.44-]2.5[B(6b)0.08+]1 )

[Mg2+]2[Rh2+]0.5[B7]4.87≈5.0-

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